This set of articles explains how the Higgs field gives mass to other particles, and some details about the Higgs particle.
These articles require the kind of math that you’d come across in advanced pre-university or beginning university settings: algebra, cosines and sines, a little calculus (though most of that can be skirted) and a little familiarity with simple physics concepts: energy, oscillations, waves. Some of this stuff is reviewed in the Particles and Fields articles in any case.
1. The Basic Idea (of how the Higgs field gives mass to other particles.)
2. Why The Higgs Field Becomes Non-Zero, unlike other fields.
3. How the Higgs Particle Arises, as a quantum of the waves in the Higgs field as it oscillates around its non-zero equilibrium value.
4. Why the Higgs Field is Necessary (why in our universe, with its weak nuclear force, the electron can’t have a mass without it.)
Before reading these articles you should first read through my set of articles on Particles and Fields, which are at the same level, and are intended to lead directly to this set.